\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]

↓

\[\begin{array}{l} \mathbf{if}\;z \le -1561166178717786600 \lor \neg \left(z \le 706881567136002.375\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + t \cdot \frac{1}{{z}^{2}}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\\ \end{array}\]

x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}

↓

\begin{array}{l}
\mathbf{if}\;z \le -1561166178717786600 \lor \neg \left(z \le 706881567136002.375\right):\\
\;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + t \cdot \frac{1}{{z}^{2}}, x\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(y \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\\

\end{array}

double f(double x, double y, double z, double t, double a, double b) {
        double r330425 = x;
        double r330426 = y;
        double r330427 = z;
        double r330428 = 3.13060547623;
        double r330429 = r330427 * r330428;
        double r330430 = 11.1667541262;
        double r330431 = r330429 + r330430;
        double r330432 = r330431 * r330427;
        double r330433 = t;
        double r330434 = r330432 + r330433;
        double r330435 = r330434 * r330427;
        double r330436 = a;
        double r330437 = r330435 + r330436;
        double r330438 = r330437 * r330427;
        double r330439 = b;
        double r330440 = r330438 + r330439;
        double r330441 = r330426 * r330440;
        double r330442 = 15.234687407;
        double r330443 = r330427 + r330442;
        double r330444 = r330443 * r330427;
        double r330445 = 31.4690115749;
        double r330446 = r330444 + r330445;
        double r330447 = r330446 * r330427;
        double r330448 = 11.9400905721;
        double r330449 = r330447 + r330448;
        double r330450 = r330449 * r330427;
        double r330451 = 0.607771387771;
        double r330452 = r330450 + r330451;
        double r330453 = r330441 / r330452;
        double r330454 = r330425 + r330453;
        return r330454;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r330455 = z;
        double r330456 = -1.5611661787177866e+18;
        bool r330457 = r330455 <= r330456;
        double r330458 = 706881567136002.4;
        bool r330459 = r330455 <= r330458;
        double r330460 = !r330459;
        bool r330461 = r330457 || r330460;
        double r330462 = y;
        double r330463 = 3.13060547623;
        double r330464 = t;
        double r330465 = 1.0;
        double r330466 = 2.0;
        double r330467 = pow(r330455, r330466);
        double r330468 = r330465 / r330467;
        double r330469 = r330464 * r330468;
        double r330470 = r330463 + r330469;
        double r330471 = x;
        double r330472 = fma(r330462, r330470, r330471);
        double r330473 = 15.234687407;
        double r330474 = r330455 + r330473;
        double r330475 = 31.4690115749;
        double r330476 = fma(r330474, r330455, r330475);
        double r330477 = 11.9400905721;
        double r330478 = fma(r330476, r330455, r330477);
        double r330479 = 0.607771387771;
        double r330480 = fma(r330478, r330455, r330479);
        double r330481 = r330465 / r330480;
        double r330482 = r330462 * r330481;
        double r330483 = 11.1667541262;
        double r330484 = fma(r330455, r330463, r330483);
        double r330485 = fma(r330484, r330455, r330464);
        double r330486 = a;
        double r330487 = fma(r330485, r330455, r330486);
        double r330488 = b;
        double r330489 = fma(r330487, r330455, r330488);
        double r330490 = fma(r330482, r330489, r330471);
        double r330491 = r330461 ? r330472 : r330490;
        return r330491;
}

Original	29.4
Target	1.2
Herbie	1.4

Derivation

Split input into 2 regimes
if z < -1.5611661787177866e+18 or 706881567136002.4 < z
1. Initial program 56.9
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
2. Simplified54.5
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)}\]
3. Taylor expanded around inf 9.3
  \[\leadsto \color{blue}{x + \left(\frac{t \cdot y}{{z}^{2}} + 3.13060547622999996 \cdot y\right)}\]
4. Simplified2.5
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{z}, \frac{t}{z}, \mathsf{fma}\left(3.13060547622999996, y, x\right)\right)}\]
5. Taylor expanded around 0 9.3
  \[\leadsto \color{blue}{x + \left(\frac{t \cdot y}{{z}^{2}} + 3.13060547622999996 \cdot y\right)}\]
6. Simplified2.4
  \[\leadsto \color{blue}{\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)}\]
7. Using strategy rm
8. Applied div-inv2.4
  \[\leadsto \mathsf{fma}\left(y, 3.13060547622999996 + \color{blue}{t \cdot \frac{1}{{z}^{2}}}, x\right)\]
if -1.5611661787177866e+18 < z < 706881567136002.4
1. Initial program 0.5
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
2. Simplified0.3
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)}\]
3. Using strategy rm
4. Applied div-inv0.4
  \[\leadsto \mathsf{fma}\left(\color{blue}{y \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\]
Recombined 2 regimes into one program.
Final simplification1.4
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1561166178717786600 \lor \neg \left(z \le 706881567136002.375\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + t \cdot \frac{1}{{z}^{2}}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :herbie-target
  (if (< z -6.499344996252632e+53) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1))) (if (< z 7.066965436914287e+59) (+ x (/ y (/ (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771) (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)))) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1)))))

  (+ x (/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))

Falling back on racket egraph because egg-herbie package not installed (more)

Error

Target

Derivation

`if z < -1.5611661787177866e+18 or 706881567136002.4 < z`

`if -1.5611661787177866e+18 < z < 706881567136002.4`

Reproduce